Summary

You searched for: Spectrum0=1/2,1,1,3/2

Your search produced 47 matches
 1-30  31-47 

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1

New Number: 2.52 |  AESZ: 16  |  Superseeker: 4 644/3  |  Hash: 05af0662662bfbec63e3186c4f363313  

Degree: 2

\(\theta^4-2^{2} x(2\theta+1)^2(5\theta^2+5\theta+2)+2^{8} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 168, 5120, 190120, ...
--> OEIS
Normalized instanton numbers (n0=1): 4, 20, 644/3, 3072, 52512, ... ; Common denominator:...

Discriminant

\((64z-1)(16z-1)\)

Local exponents

\(0\)\(\infty\)\(\frac{ 1}{ 16}\)\(\frac{ 1}{ 64}\)
\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(2\)\(2\)

Note:

Hadamard product $I \ast \alpha$
A-Incarnation: diagonal subfamily of 1,1,1,1-intersection in $P^1 \times P^1 \times P^1 \times \P^1$
B-Incarnations:
Fibre products: 62211- x 632--1, S62211

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2

New Number: 2.53 |  AESZ: 29  |  Superseeker: 14 10424/3  |  Hash: 92e8a038051b3fb8e0cc6ad6a52b8bfb  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(17\theta^2+17\theta+5)+2^{2} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 438, 28900, 2310070, ...
--> OEIS
Normalized instanton numbers (n0=1): 14, 303/2, 10424/3, 113664, 4579068, ... ; Common denominator:...

Discriminant

\(1-136z+16z^2\)

Local exponents

\(0\)\(\frac{ 17}{ 4}+3\sqrt{ 2}\)\(\frac{ 17}{ 4}-3\sqrt{ 2}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \gamma$

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3

New Number: 2.54 |  AESZ: 41  |  Superseeker: 2 -104  |  Hash: a9ddeed4299f59fb9ac9f6f248383b8f  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(7\theta^2+7\theta+3)+2^{2} 3^{4} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 54, 60, -19530, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, -7, -104, -588, 3300, ... ; Common denominator:...

Discriminant

\(1-56z+1296z^2\)

Local exponents

\(0\)\(\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)\(\infty\)\(\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)

Note:

Hadamard product $I \ast \delta$

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4

New Number: 2.55 |  AESZ: 42  |  Superseeker: 8 1000  |  Hash: c389d3bc0e31801bc4b7b3e186702bc9  

Degree: 2

\(\theta^4-2^{3} x(2\theta+1)^2(3\theta^2+3\theta+1)+2^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 240, 10880, 597520, ...
--> OEIS
Normalized instanton numbers (n0=1): 8, 63, 1000, 44369/2, 606168, ... ; Common denominator:...

Discriminant

\(1-96z+256z^2\)

Local exponents

\(0\)\(\infty\)\(\frac{ 3}{ 16}-\frac{ 1}{ 8}\sqrt{ 2}\)\(\frac{ 3}{ 16}+\frac{ 1}{ 8}\sqrt{ 2}\)
\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(2\)\(2\)

Note:

Hadamard product $I \ast \epsilon$

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5

New Number: 2.56 |  AESZ: 185  |  Superseeker: 6 608  |  Hash: 80506439e4d4fdc41f5b16e246a69fbf  

Degree: 2

\(\theta^4-2 3 x(2\theta+1)^2(3\theta^2+3\theta+1)-2^{2} 3^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 6180, 284130, ...
--> OEIS
Normalized instanton numbers (n0=1): 6, 93/2, 608, 11754, 275352, ... ; Common denominator:...

Discriminant

\(1-72z-432z^2\)

Local exponents

\(-\frac{ 1}{ 12}-\frac{ 1}{ 18}\sqrt{ 3}\)\(0\)\(-\frac{ 1}{ 12}+\frac{ 1}{ 18}\sqrt{ 3}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(1\)\(0\)\(1\)\(1\)
\(1\)\(0\)\(1\)\(1\)
\(2\)\(0\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \zeta$

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6

New Number: 2.57 |  AESZ: 184  |  Superseeker: 2 -8  |  Hash: ee8bb517b329e58eeb4352dc3cdc3f81  

Degree: 2

\(\theta^4-2 x(2\theta+1)^2(11\theta^2+11\theta+5)+2^{2} 5^{3} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 210, 5500, 159250, ...
--> OEIS
Normalized instanton numbers (n0=1): 2, 4, -8, -194, -2820, ... ; Common denominator:...

Discriminant

\(1-88z+2000z^2\)

Local exponents

\(0\)\(\frac{ 11}{ 500}+\frac{ 1}{ 250}I\)\(\infty\)\(\frac{ 11}{ 500}-\frac{ 1}{ 250}I\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)

Note:

Hadamard product $I \ast \eta$

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7

New Number: 2.58 |  AESZ: 46  |  Superseeker: -6 -104  |  Hash: 2226ec115674e71c483ba2c0350e8adf  

Degree: 2

\(\theta^4-2 3 x(2\theta+1)^2(9\theta^2+9\theta+5)+2^{2} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 1782, 129900, 10463670, ...
--> OEIS
Normalized instanton numbers (n0=1): -6, -6, -104, 36, -4812, ... ; Common denominator:...

Discriminant

\((108z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 108}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(\frac{ 1}{ 6}\)\(1\)
\(0\)\(\frac{ 5}{ 6}\)\(1\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \iota$

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8

New Number: 2.59 |  AESZ: 47  |  Superseeker: -384 -164736  |  Hash: 792da990d2d2e5263bb789ad37b00d44  

Degree: 2

\(\theta^4-2^{4} 3 x(2\theta+1)^2(18\theta^2+18\theta+13)+2^{10} 3^{6} x^{2}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 624, 685584, 883925760, 1229988226320, ...
--> OEIS
Normalized instanton numbers (n0=1): -384, -1356, -164736, 96211836, -3267254400, ... ; Common denominator:...

Discriminant

\((1728z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 1728}\)\(\infty\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(-\frac{ 1}{ 6}\)\(1\)
\(0\)\(1\)\(1\)
\(0\)\(\frac{ 7}{ 6}\)\(\frac{ 3}{ 2}\)

Note:

Hadamard product $I \ast \kappa$

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9

New Number: 4.35 |  AESZ:  |  Superseeker: -16 -1744  |  Hash: cd392ce4c33f242f5d17e59976d0ea4f  

Degree: 4

\(\theta^4-2^{4} x\left(23\theta^4+14\theta^3+13\theta^2+6\theta+1\right)+2^{11} x^{2}\theta(21\theta^3+24\theta^2+18\theta+4)-2^{16} x^{3}(2\theta+1)(10\theta^3+7\theta^2-5\theta-4)-2^{23} x^{4}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 912, 67840, 5839120, ...
--> OEIS
Normalized instanton numbers (n0=1): -16, -106, -1744, -29526, -644016, ... ; Common denominator:...

Discriminant

\(-(16z+1)(128z-1)^3\)

Local exponents

\(0\)\(-\frac{ 1}{ 16}\)\(\frac{ 1}{ 128}\)\(\infty\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(\frac{ 3}{ 2}\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)

Note:

Operator equivalent to 3.34, equivalent to
AESZ 107 $=d \ast d$.

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10

New Number: 5.107 |  AESZ: 364  |  Superseeker: 11/5 71/5  |  Hash: c5b4bc60bc9d39ea420bd49fad182557  

Degree: 5

\(5^{2} \theta^4-5 x\left(553\theta^4+722\theta^3+611\theta^2+250\theta+40\right)+2^{6} x^{2}\left(1914\theta^4+4722\theta^3+5519\theta^2+3010\theta+610\right)-2^{12} x^{3}\left(685\theta^4+2400\theta^3+3466\theta^2+2220\theta+500\right)+2^{19} x^{4}(2\theta+1)(30\theta^3+105\theta^2+122\theta+46)-2^{25} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 120, 2240, 50680, ...
--> OEIS
Normalized instanton numbers (n0=1): 11/5, -8/5, 71/5, 738, 26841/5, ... ; Common denominator:...

Discriminant

\(-(32768z^3-2560z^2+85z-1)(-5+64z)^2\)

Local exponents

\(0\) ≈\(0.023029\)\(\frac{ 5}{ 64}\)\(\infty\) ≈\(0.027548+0.023797I\) ≈\(0.027548-0.023797I\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)\(2\)\(2\)

Note:

This is operator "5.107" from ...

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11

New Number: 5.109 |  AESZ: 373  |  Superseeker: 50 68472  |  Hash: 8b0fbfc0016c3fb02fd42d4ff919e0f8  

Degree: 5

\(\theta^4-2 x\left(190\theta^4+308\theta^3+227\theta^2+73\theta+9\right)+2^{2} x^{2}\left(4780\theta^4+6304\theta^3+2395\theta^2+642\theta+135\right)-2^{4} 3 x^{3}\left(6700\theta^4+8472\theta^3+7607\theta^2+3615\theta+648\right)+2^{7} 3^{2} x^{4}(2\theta+1)(760\theta^3+1464\theta^2+1211\theta+375)-2^{10} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 18, 1782, 276660, 52396470, ...
--> OEIS
Normalized instanton numbers (n0=1): 50, 1299, 68472, 5536032, 555252324, ... ; Common denominator:...

Discriminant

\(-(-1+324z)(24z-1)^2(4z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 324}\)\(\frac{ 1}{ 24}\)\(\frac{ 1}{ 4}\)\(\infty\)
\(0\)\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)
\(0\)\(1\)\(1\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(1\)\(3\)\(\frac{ 1}{ 2}\)\(1\)
\(0\)\(2\)\(4\)\(1\)\(\frac{ 3}{ 2}\)

Note:

This is operator "5.109" from ...

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12

New Number: 5.114 |  AESZ: 412  |  Superseeker: -1312 -127846048  |  Hash: 4a9870395db313fa368bbafcfc6a7435  

Degree: 5

\(\theta^4-2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)-2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)-2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 240, 118032, 72810240, 50454043920, ...
--> OEIS
Normalized instanton numbers (n0=1): -1312, -301048, -127846048, -70845744192, -45645879602784, ... ; Common denominator:...

Discriminant

\(-(-1+768z)(3072z-1)^2(1024z-1)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 768}\)\(\frac{ 1}{ 1024}\)\(\infty\)\(\frac{ 1}{ 3072}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(3\)
\(0\)\(2\)\(1\)\(\frac{ 3}{ 2}\)\(4\)

Note:

B-Incarnation as double octic D.O.256

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13

New Number: 5.118 |  AESZ: 416  |  Superseeker: 1312 127846048  |  Hash: 3ae3241981d64d9c9cc38b29974fa202  

Degree: 5

\(\theta^4+2^{4} x\left(560\theta^4-32\theta^3+56\theta^2+72\theta+15\right)+2^{15} x^{2}\left(896\theta^4+272\theta^3+604\theta^2+196\theta+21\right)+2^{24} 3^{2} x^{3}\left(288\theta^4+352\theta^3+364\theta^2+164\theta+29\right)+2^{35} 3^{3} x^{4}(2\theta+1)(16\theta^3+32\theta^2+28\theta+9)+2^{46} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -240, 118032, -72810240, 50454043920, ...
--> OEIS
Normalized instanton numbers (n0=1): 1312, -301376, 127846048, -70845744192, 45645879602784, ... ; Common denominator:...

Discriminant

\((1+768z)(1024z+1)^2(3072z+1)^2\)

Local exponents

\(0\)\(\infty\)\(-\frac{ 1}{ 1024}\)\(-\frac{ 1}{ 3072}\)\(-\frac{ 1}{ 768}\)
\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(1\)\(1\)
\(0\)\(1\)\(\frac{ 1}{ 2}\)\(3\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(1\)\(4\)\(2\)

Note:

This is operator "5.118" from ...

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14

New Number: 5.119 |  AESZ:  |  Superseeker: 138 278872  |  Hash: 61d7a82df3cf3c429b6286bc39ccb426  

Degree: 5

\(\theta^4-2 3 x\left(42\theta^4+204\theta^3+145\theta^2+43\theta+5\right)-2^{2} x^{2}\left(26932\theta^4+40768\theta^3-6943\theta^2-8482\theta-1635\right)-2^{4} 3^{2} 5 x^{3}\left(11156\theta^4+3848\theta^3+1777\theta^2+901\theta+180\right)-2^{7} 3^{3} 5^{2} x^{4}(2\theta+1)(304\theta^3+356\theta^2+97\theta-15)+2^{10} 3^{3} 5^{5} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 30, 4530, 1074900, 312527250, ...
--> OEIS
Normalized instanton numbers (n0=1): 138, 1139, 278872, 21493934, 3832908140, ... ; Common denominator:...

Discriminant

\((4z-1)(500z-1)(12z+1)(1+120z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 4}\)\(\infty\)\(-\frac{ 1}{ 12}\)\(-\frac{ 1}{ 120}\)\(\frac{ 1}{ 500}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(4\)\(2\)

Note:

This is operator "5.119" from ...

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15

New Number: 5.120 |  AESZ:  |  Superseeker: 48 171120  |  Hash: 3eb6b52ff225f7b2f94716d73344b578  

Degree: 5

\(\theta^4-2^{4} x\left(41\theta^4+34\theta^3+25\theta^2+8\theta+1\right)+2^{10} x^{2}\left(126\theta^4+108\theta^3+33\theta^2+6\theta+1\right)-2^{14} x^{3}\left(564\theta^4+504\theta^3+429\theta^2+195\theta+34\right)+2^{21} x^{4}(2\theta+1)(44\theta^3+78\theta^2+59\theta+17)-2^{28} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 16, 1680, 298240, 64975120, ...
--> OEIS
Normalized instanton numbers (n0=1): 48, 2286, 171120, 17540830, 2229934864, ... ; Common denominator:...

Discriminant

\(-(16z-1)(4096z^2-384z+1)(-1+128z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 64}-\frac{ 1}{ 32}\sqrt{ 2}\)\(\infty\)\(\frac{ 3}{ 64}+\frac{ 1}{ 32}\sqrt{ 2}\)\(\frac{ 1}{ 128}\)\(\frac{ 1}{ 16}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(4\)\(2\)

Note:

B-Incarnation as fibre product 62211- x 821--1

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16

New Number: 5.121 |  AESZ:  |  Superseeker: 272 1143760  |  Hash: 36da1ed5dd29b416116a3ac9f4b4c4da  

Degree: 5

\(\theta^4-2^{4} x\left(17\theta^4+130\theta^3+91\theta^2+26\theta+3\right)-2^{11} x^{2}\left(150\theta^4+204\theta^3-163\theta^2-110\theta-21\right)-2^{16} x^{3}\left(564\theta^4-648\theta^3-595\theta^2-189\theta-18\right)+2^{24} x^{4}(2\theta+1)(52\theta^3+66\theta^2+29\theta+3)-2^{32} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 10128, 3521280, 1516853520, ...
--> OEIS
Normalized instanton numbers (n0=1): 272, -142, 1143760, 76778666, 28997783216, ... ; Common denominator:...

Discriminant

\(-(16z-1)(16384z^2-768z+1)(1+256z)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 128}-\frac{ 1}{ 64}\sqrt{ 2}\)\(\infty\)\(\frac{ 1}{ 16}\)\(-\frac{ 1}{ 256}\)\(\frac{ 3}{ 128}+\frac{ 1}{ 64}\sqrt{ 2}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(4\)\(2\)

Note:

B-Incarnation as fibre product 62211- x 182--1

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17

New Number: 5.122 |  AESZ:  |  Superseeker: 19 18641/3  |  Hash: 7cc1a0411f21ffd93f1a9f6468627432  

Degree: 5

\(\theta^4+x\left(119\theta^4-194\theta^3-143\theta^2-46\theta-6\right)-2^{2} 3^{2} x^{2}\left(46\theta^4+748\theta^3+379\theta^2+150\theta+27\right)-2^{2} 3^{4} x^{3}\left(2164\theta^4+6264\theta^3+7421\theta^2+4131\theta+846\right)-2^{5} 3^{8} x^{4}(2\theta+1)(76\theta^3+222\theta^2+235\theta+85)-2^{8} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 6, 162, 7620, 334530, ...
--> OEIS
Normalized instanton numbers (n0=1): 19, -170, 18641/3, -163734, 6446745, ... ; Common denominator:...

Discriminant

\(-(81z-1)(1296z^2+56z+1)(1+72z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(\infty\)\(-\frac{ 1}{ 72}\)\(-\frac{ 7}{ 324}+\frac{ 1}{ 81}\sqrt{ 2}I\)\(-\frac{ 7}{ 324}-\frac{ 1}{ 81}\sqrt{ 2}I\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(4\)\(2\)\(2\)

Note:

B-Incarnation as fibre product 62211- 623--1

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18

New Number: 5.123 |  AESZ:  |  Superseeker: 96 266464  |  Hash: b9a4a4eae678c9ce13a407517f92c30e  

Degree: 5

\(\theta^4+2^{4} x\left(28\theta^4-40\theta^3-28\theta^2-8\theta-1\right)+2^{13} x^{2}\left(6\theta^4-12\theta^3+17\theta^2+10\theta+2\right)+2^{18} x^{3}\left(12\theta^4+72\theta^3+35\theta^2-3\theta-4\right)+2^{26} x^{4}(2\theta+1)(4\theta^3-6\theta^2-15\theta-7)-2^{34} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 16, -240, -24320, 2075920, ...
--> OEIS
Normalized instanton numbers (n0=1): 96, -4200, 266464, -20295944, 1778341408, ... ; Common denominator:...

Discriminant

\(-(64z-1)(16384z^2+1)(1+256z)^2\)

Local exponents

\(0\)\(\infty\)\(\frac{ 1}{ 64}\)\(0-\frac{ 1}{ 128}I\)\(0+\frac{ 1}{ 128}I\)\(-\frac{ 1}{ 256}\)
\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(2\)\(4\)

Note:

B-Incarnation as fibre product 62211- x 812--1

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19

New Number: 5.124 |  AESZ:  |  Superseeker: 307 4336475  |  Hash: 782c2ecb639a2462baac59dfaf17de0e  

Degree: 5

\(\theta^4-x\left(1081\theta^4+2594\theta^3+1807\theta^2+510\theta+54\right)-2^{2} 3^{2} x^{2}\left(4686\theta^4+4908\theta^3-2213\theta^2-1738\theta-293\right)-2^{2} 3^{4} x^{3}\left(18484\theta^4-3336\theta^3-4883\theta^2-1101\theta-50\right)+2^{5} 3^{7} x^{4}(2\theta+1)(92\theta^3+134\theta^2+79\theta+17)-2^{8} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 54, 19746, 11427300, 8114331330, ...
--> OEIS
Normalized instanton numbers (n0=1): 307, 19410, 4336475, 1291393654, 484327566649, ... ; Common denominator:...

Discriminant

\(-(z-1)(1296z^2-1224z+1)(1+72z)^2\)

Local exponents

\(0\)\(1\)\(\frac{ 17}{ 36}+\frac{ 1}{ 3}\sqrt{ 2}\)\(\infty\)\(-\frac{ 1}{ 72}\)\(\frac{ 17}{ 36}-\frac{ 1}{ 3}\sqrt{ 2}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)\(4\)\(2\)

Note:

B-Incarnation as fibre product 62211- x 263--1

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20

New Number: 5.125 |  AESZ:  |  Superseeker: 229 10128562/3  |  Hash: ce147b64cc67dee1204a2d16f6ac4210  

Degree: 5

\(\theta^4-x\left(1217\theta^4+2050\theta^3+1437\theta^2+412\theta+44\right)+2^{5} x^{2}(\theta+1)(4550\theta^3-186\theta^2-899\theta-171)-2^{8} x^{3}\left(18484\theta^4+3192\theta^3+1005\theta^2+1107\theta+258\right)+2^{14} x^{4}(2\theta+1)(268\theta^3+414\theta^2+267\theta+65)-2^{20} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

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Coefficients of the holomorphic solution: 1, 44, 14532, 7508960, 4749338020, ...
--> OEIS
Normalized instanton numbers (n0=1): 229, 18542, 10128562/3, 938391582, 323686899951, ... ; Common denominator:...

Discriminant

\(-(z-1)(1024z^2-1088z+1)(-1+64z)^2\)

Local exponents

\(0\)\(1\)\(\frac{ 17}{ 32}+\frac{ 3}{ 8}\sqrt{ 2}\)\(\infty\)\(\frac{ 17}{ 32}-\frac{ 3}{ 8}\sqrt{ 2}\)\(\frac{ 1}{ 64}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(4\)

Note:

B-Incarnation as fibre product 62211- x 362--1

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21

New Number: 5.131 |  AESZ:  |  Superseeker: 325 9106834/3  |  Hash: 79657f8be76c1fed5fd1a658989ca15a  

Degree: 5

\(\theta^4-x\left(60+460\theta+1565\theta^2+2210\theta^3-623\theta^4\right)-2^{5} 3^{2} x^{2}\left(550\theta^4+2764\theta^3-3581\theta^2-2190\theta-459\right)-2^{8} 3^{4} x^{3}\left(2164\theta^4-17928\theta^3-13315\theta^2-3645\theta-126\right)+2^{14} 3^{8} x^{4}(2\theta+1)(148\theta^3+114\theta^2-35\theta-41)-2^{20} 3^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 60, 5508, 362400, -34621020, ...
--> OEIS
Normalized instanton numbers (n0=1): 325, -24254, 9106834/3, -514805406, 102077718255, ... ; Common denominator:...

Discriminant

\(-(81z-1)(82944z^2-448z+1)(1+576z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 81}\)\(-\frac{ 1}{ 576}\)\(\infty\)\(\frac{ 7}{ 2592}+\frac{ 1}{ 648}\sqrt{ 2}I\)\(\frac{ 7}{ 2592}-\frac{ 1}{ 648}\sqrt{ 2}I\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)\(2\)\(2\)

Note:

B-Incarnation as fibre product 62211- x 326--1

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22

New Number: 5.132 |  AESZ:  |  Superseeker: 388 3446444  |  Hash: 55a5cb23b8c035363ff67bcc0d5fd556  

Degree: 5

\(\theta^4+2^{2} x\left(92\theta^4-680\theta^3-481\theta^2-141\theta-18\right)-2^{8} 3^{2} x^{2}\left(192\theta^4+456\theta^3-514\theta^2-323\theta-67\right)-2^{14} 3^{4} x^{3}\left(88\theta^4-312\theta^3-248\theta^2-75\theta-5\right)+2^{20} 3^{7} x^{4}(2\theta+1)(8\theta^3+8\theta^2+\theta-1)-2^{26} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 72, 12456, 3202560, 1030375080, ...
--> OEIS
Normalized instanton numbers (n0=1): 388, -23196, 3446444, -571523888, 119779121440, ... ; Common denominator:...

Discriminant

\(-(144z-1)(576z-1)(64z-1)(1+576z)^2\)

Local exponents

\(0\)\(\frac{ 1}{ 144}\)\(-\frac{ 1}{ 576}\)\(\infty\)\(\frac{ 1}{ 64}\)\(\frac{ 1}{ 576}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(3\)\(1\)\(1\)\(1\)
\(0\)\(2\)\(4\)\(\frac{ 3}{ 2}\)\(2\)\(2\)

Note:

B-Incarnation as fibre product 62211- x 236--1

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23

New Number: 5.133 |  AESZ:  |  Superseeker: 192 1016256  |  Hash: 0f3cb34d2bc462fbc58cdf15040595d1  

Degree: 5

\(\theta^4+2^{4} x\left(24\theta^4-96\theta^3-70\theta^2-22\theta-3\right)-2^{10} x^{2}\left(124\theta^4+496\theta^3-271\theta^2-202\theta-45\right)-2^{17} 3^{2} x^{3}\left(32\theta^4-56\theta^3-66\theta^2-31\theta-5\right)+2^{24} 3^{3} x^{4}(\theta+1)(2\theta+1)(6\theta^2+11\theta+6)+2^{32} 3^{3} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 48, 5136, 710400, 112104720, ...
--> OEIS
Normalized instanton numbers (n0=1): 192, -9940, 1016256, -134713756, 20854352960, ... ; Common denominator:...

Discriminant

\((256z-1)(64z+1)(192z-1)(1+384z)^2\)

Local exponents

\(0\)\(-\frac{ 1}{ 64}\)\(\infty\)\(\frac{ 1}{ 192}\)\(\frac{ 1}{ 256}\)\(-\frac{ 1}{ 384}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(4\)

Note:

B-incarnation as self-fibre product S53211

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24

New Number: 5.17 |  AESZ: 119  |  Superseeker: 28/3 3892/3  |  Hash: dc8ec37012f2c92c83e6519935956eeb  

Degree: 5

\(3^{2} \theta^4-2^{2} 3 x\left(256\theta^4+320\theta^3+271\theta^2+111\theta+18\right)+2^{7} x^{2}\left(3104\theta^4+7040\theta^3+8012\theta^2+4452\theta+927\right)-2^{15} x^{3}\left(752\theta^4+2304\theta^3+3042\theta^2+1854\theta+405\right)+2^{21} x^{4}(2\theta+1)(176\theta^3+552\theta^2+622\theta+231)-2^{31} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 24, 1128, 67200, 4634280, ...
--> OEIS
Normalized instanton numbers (n0=1): 28/3, 394/3, 3892/3, 108262/3, 1044128, ... ; Common denominator:...

Discriminant

\(-(-1+128z)(64z-1)^2(128z-3)^2\)

Local exponents

\(0\)\(\frac{ 3}{ 128}\)\(\frac{ 1}{ 128}\)\(\infty\)\(\frac{ 1}{ 64}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(\frac{ 1}{ 4}\)
\(0\)\(3\)\(1\)\(1\)\(\frac{ 3}{ 4}\)
\(0\)\(4\)\(2\)\(\frac{ 3}{ 2}\)\(1\)

Note:

This is operator "5.17" from ...

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25

New Number: 5.30 |  AESZ: 209  |  Superseeker: 478/17 285760/17  |  Hash: a03a0a18a8b2a4926d11e4e42b958f98  

Degree: 5

\(17^{2} \theta^4-2 17 x\left(1902\theta^4+3708\theta^3+2789\theta^2+935\theta+119\right)+2^{2} x^{2}\left(62408\theta^4+68576\theta^3-10029\theta^2-24106\theta-5661\right)-2^{2} x^{3}\left(66180\theta^4+33048\theta^3+20785\theta^2+17799\theta+4794\right)+2^{7} x^{4}(2\theta+1)(196\theta^3+498\theta^2+487\theta+169)-2^{12} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 14, 978, 103820, 13387570, ...
--> OEIS
Normalized instanton numbers (n0=1): 478/17, 7784/17, 285760/17, 15280156/17, 1006004774/17, ... ; Common denominator:...

Discriminant

\(-(16z^3-32z^2+220z-1)(-17+32z)^2\)

Local exponents

\(0\) ≈\(0.997726-3.570079I\)\(\infty\) ≈\(0.004548\) ≈\(0.997726+3.570079I\)\(\frac{ 17}{ 32}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(4\)

Note:

This is operator "5.30" from ...

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26

New Number: 5.39 |  AESZ: 224  |  Superseeker: 59/5 22503/5  |  Hash: ba17e8cb074bba75e7a27206be530698  

Degree: 5

\(5^{2} \theta^4-5 x\left(1057\theta^4+1058\theta^3+819\theta^2+290\theta+40\right)+2^{5} x^{2}\left(10123\theta^4+11419\theta^3+5838\theta^2+1510\theta+180\right)-2^{8} x^{3}\left(30981\theta^4+46560\theta^3+48211\theta^2+25500\theta+5100\right)+2^{14} 11 x^{4}(2\theta+1)(234\theta^3+591\theta^2+581\theta+202)-2^{20} 11^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 312, 19520, 1475320, ...
--> OEIS
Normalized instanton numbers (n0=1): 59/5, 186, 22503/5, 718052/5, 29091017/5, ... ; Common denominator:...

Discriminant

\(-(128z-1)(128z^2-13z+1)(-5+176z)^2\)

Local exponents

\(0\)\(\frac{ 13}{ 256}-\frac{ 7}{ 256}\sqrt{ 7}I\)\(\frac{ 13}{ 256}+\frac{ 7}{ 256}\sqrt{ 7}I\)\(\infty\)\(\frac{ 1}{ 128}\)\(\frac{ 5}{ 176}\)
\(0\)\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(2\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(4\)

Note:

This is operator "5.39" from ...

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27

New Number: 5.43 |  AESZ: 234  |  Superseeker: 18/7 5676/7  |  Hash: 3e70b30959c0c3bd799b435b9c842186  

Degree: 5

\(7^{2} \theta^4-2 7 x\theta(192\theta^3+60\theta^2+37\theta+7)-2^{2} x^{2}\left(17608\theta^4+115144\theta^3+166715\theta^2+94556\theta+18816\right)+2^{4} 3^{2} x^{3}\left(20288\theta^4+57288\theta^3+27524\theta^2-7455\theta-5026\right)-2^{6} 3^{5} x^{4}(2\theta+1)(458\theta^3-657\theta^2-1799\theta-846)-2^{12} 3^{8} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 0, 96, 1440, 90720, ...
--> OEIS
Normalized instanton numbers (n0=1): 18/7, 515/7, 5676/7, 133796/7, 2929726/7, ... ; Common denominator:...

Discriminant

\(-(64z-1)(36z+1)(4z+1)(-7+108z)^2\)

Local exponents

\(0\)\(\infty\)\(\frac{ 1}{ 64}\)\(-\frac{ 1}{ 4}\)\(\frac{ 7}{ 108}\)\(-\frac{ 1}{ 36}\)
\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(3\)\(1\)
\(0\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(4\)\(2\)

Note:

This is operator "5.43" from ...

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28

New Number: 5.55 |  AESZ: 261  |  Superseeker: -76/5 -24836/5  |  Hash: adadb5e720011482371f48cfa73dab99  

Degree: 5

\(5^{2} \theta^4+2^{2} 5 x\left(292\theta^4+368\theta^3+289\theta^2+105\theta+15\right)+2^{4} x^{2}\left(24736\theta^4+43648\theta^3+38936\theta^2+18980\theta+3735\right)+2^{9} 3^{2} x^{3}\left(2512\theta^4+5760\theta^3+6328\theta^2+3330\theta+655\right)+2^{12} 3^{4} x^{4}(2\theta+1)(232\theta^3+588\theta^2+590\theta+207)+2^{18} 3^{6} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, -12, 492, -32880, 2743020, ...
--> OEIS
Normalized instanton numbers (n0=1): -76/5, 1103/5, -24836/5, 847456/5, -36542448/5, ... ; Common denominator:...

Discriminant

\((1+144z)(16z+1)^2(144z+5)^2\)

Local exponents

\(-\frac{ 1}{ 144}\)\(-\frac{ 1}{ 16}\)\(\infty\)\(0\)\(-\frac{ 5}{ 144}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(1\)
\(1\)\(\frac{ 1}{ 2}\)\(1\)\(0\)\(3\)
\(2\)\(1\)\(\frac{ 3}{ 2}\)\(0\)\(4\)

Note:

This is operator "5.55" from ...

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29

New Number: 5.70 |  AESZ: 287  |  Superseeker: 361/21 120472/21  |  Hash: 97932196c46a8712f6dcb11165d698be  

Degree: 5

\(3^{2} 7^{2} \theta^4-3 7 x\left(3289\theta^4+6098\theta^3+4645\theta^2+1596\theta+210\right)+2^{2} 5 x^{2}\left(7712\theta^4-46168\theta^3-106885\theta^2-67410\theta-13629\right)+2^{4} x^{3}\left(106636\theta^4+493416\theta^3+420211\theta^2+116361\theta+6090\right)-2^{8} 5 x^{4}(2\theta+1)(1916\theta^3+2622\theta^2+1077\theta+91)-2^{12} 5^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 10, 510, 38260, 3473470, ...
--> OEIS
Normalized instanton numbers (n0=1): 361/21, 4780/21, 120472/21, 1537864/7, 216261320/21, ... ; Common denominator:...

Discriminant

\(-(64z^3+800z^2+149z-1)(-21+80z)^2\)

Local exponents

\(0\) ≈\(0.006485\)\(\infty\)\(\frac{ 21}{ 80}\) ≈\(-12.310784\) ≈\(-0.195701\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(3\)\(1\)\(1\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(4\)\(2\)\(2\)

Note:

This is operator "5.70" from ...

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30

New Number: 5.73 |  AESZ: 293  |  Superseeker: 20 13188  |  Hash: f19eeaee48396d15d7cf7be47d7d48a7  

Degree: 5

\(\theta^4-2^{2} x\left(54\theta^4+66\theta^3+49\theta^2+16\theta+2\right)+2^{4} x^{2}\left(417\theta^4-306\theta^3-1219\theta^2-776\theta-154\right)+2^{8} x^{3}\left(166\theta^4+1920\theta^3+1589\theta^2+432\theta+23\right)-2^{12} 7 x^{4}(2\theta+1)(38\theta^3+45\theta^2+12\theta-2)-2^{14} 7^{2} x^{5}(2\theta+1)(\theta+1)^2(2\theta+3)\)

Maple   LaTex

Coefficients of the holomorphic solution: 1, 8, 528, 45440, 4763920, ...
--> OEIS
Normalized instanton numbers (n0=1): 20, 867/2, 13188, 609734, 35512476, ... ; Common denominator:...

Discriminant

\(-(16z+1)(256z^2+176z-1)(-1+28z)^2\)

Local exponents

\(0\)\(-\frac{ 1}{ 16}\)\(\infty\)\(-\frac{ 11}{ 32}-\frac{ 5}{ 32}\sqrt{ 5}\)\(-\frac{ 11}{ 32}+\frac{ 5}{ 32}\sqrt{ 5}\)\(\frac{ 1}{ 28}\)
\(0\)\(0\)\(\frac{ 1}{ 2}\)\(0\)\(0\)\(0\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(1\)
\(0\)\(1\)\(1\)\(1\)\(1\)\(3\)
\(0\)\(2\)\(\frac{ 3}{ 2}\)\(2\)\(2\)\(4\)

Note:

This is operator "5.73" from ...

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